Export like in texture view?
It's because the material isn't exported (except its name and mesh assignment basically). Anyway, as long as you change the rendering engine you have to change the material, interoperability is rare in this context.

Once in Unity, the material might be here among your assets, with the same name as in Blender, but with blank default parameters. You will have to set its settings properly and assign its maps (which might also need to be imported first).